SOME DUAL KINEMATIC FORMULAS

In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.

A Kinematic Formula for Integral Invariant of Degree 4 in Real Space Form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.

Kinematic Formulas of Total Mean Curvatures for Hypersurfaces

kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space

ON THE SUFFICIENT CONDITION FOR A CONVEX DOMAIN TO CONTAIN ANOTHER IN R_(2n)

In this paper, the author extends Ren's results in plane to the case of R2n,i.e., estimates the kinematic measure of a convex domain D1 with boundary Σ1 moving to another domain D0 with boundary Σ0 under the isometry group G in R2n. A sufficient condition for D0 contain D1 by using kinematic foundamatal formula and Poincare's formula in Rn is obtained.

The Kinematic Density for Pairs of Intersecting Lines

In this paper, we get a kinematic density formula for pairs of intersecting lines which has not yet been gotten in integral geometry by using the moving orthogonal frames method. And we obtain a kinematic formula of the intersection of the pairs of intersecting lines belonging to convex body K by using it.

The Bonnesen isoperimetric inequality in a surface of constant curvature

We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.

The Willmore functional and the containment problem in R^4

Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.